Generalization of the Overlapping Coefficient for k ≥ 2 Normal Distributions

Department of Statistics, Yarmouk University, Irbid, Jordan

^* Corresponding author: omarm@yu.edu.jo

Received: 4 November 2024
Accepted: 13 February 2025

Abstract

The overlapping coefficients are the measures of homogeneity or closeness between two distributions. There are several coefficients in the literature including theWeitzman coefficient Δ, which represents the area of intersection between two distributions. In this paper, the Weitzman coefficient is generalized for k ≥ 2 distributions and then several estimators for Δ were developed assuming k normal distributions. The derivation of the new estimators was done by adopting a new general approach, which relies on modeling the overlapping coefficient as the expectation of some functions, and then the resulting expectation is estimated by using the moments method. The behavior of the resulting estimators has been investigated and compared by Monte-Carlo simulation technique. Simulation results indicated the good properties of the resulting estimators.